After studying this course, you should be able to:

• create simple models, given a clear statement of the problem

• identify the simplifying assumptions that underpin a model

• identify the key variables and the parameters of a model

• apply the input–output principle to obtain a mathematical model, where appropriate.

Author(s): The Open University

The sum of the angles of any triangle is 180°. This property can be demonstrated in several ways. One way is to draw a triangle on a piece of paper, mark each angle with a different symbol, and then cut out the angles and arrange them side by side, touching one another as illustrated.

Author(s): The Open University

## Question 1

Draw a line of symmetry on each of the shapes below.

There is another kind of symmetry which is often used in designs. It can be seen, for instance, in a car wheel trim.

Look at the trim on the left. It does not have line symmetry but
Author(s): The Open University

Two straight lines that do not intersect, no matter how far they are extended, are said to be parallel. Arrows are used to indicate parallel lines.

Author(s): The Open University

When two straight lines cross, they form four angles. In the diagram below, these angles are labelled α, β, θ and φ and referred to as alpha, beta, theta and phi. The angles opposite each other are equal. They are called vertically opposite angles. Here α and β are a pair of vertically opposite angles, as are θ and φ. Although such angles are called ‘vertically opposite’, they do not need to be vertically above and bel
Author(s): The Open University

## Question 1

A company carried out a survey, recording how staff in a particular office spent their working time. The table shows the average number of minutes spent in each hour on various activities.

Author(s): The Open University

You can use the fact that the sum of angles at a point is 360° to draw a pie chart.

## Example 4

Over a five-year period a mathematics tutor found that 16 of her students gained distinctions, 32 gained pass grades and 12 failed to complete the course. Draw a pie chart to re
Author(s): The Open University

## Activity 14

A piece of computer software is to be developed by a team of programmers. It is estimated that a team of four people would take a year. Which of the following times is the length of time taken by three program
Author(s): The Open University

Climate change: transitions to sustainability
Human societies have to take urgent action to end their dependences on fossil fuels. We have to alter the whole path of our development and decision making in order to make our societies both environmentally adaptable and sustainable. This free course, Climate change, takes on the task of trying to chart some of the ways in which it might be possible.Author(s): Creator not set

The frozen planet
This free course is a general introduction to the frozen planet, including the temperature in the polar regions; the energy from the Sun and the seasons; reading and understanding graphs and maps; and how the Arctic and Antarctic regions are defined. First published on Thu, 23 May 2019 as Author(s): Creator not set

Water for life
Atoms, elements and molecules are the building blocks of everything that makes up our world, including ourselves. In this free course, Water for life, you will learn the basic chemistry of how these components work together, starting with a chemical compound we are all very familiar with water. First published on Wed, 17 Jan 2018 as Author(s): Creator not set

Life in the Palaeozoic
Fossils are a glimpse into the distant past and fascinate young and old alike. This free course, Life in the Palaeozoic, will introduce you to the explosion of evolution that took place during the Palaeozoic era. You will look at the many different types of creatures that existed at that time and how they managed to evolve to exist on land. First published on W
Author(s): Creator not set

Water in the UK
Water is arguably the most important physical resource as it is the one that is essential to human survival. Understanding the global water cycle and how we use water is essential to planning a sustainable source of water for the future. Globally, there are many areas that do not have enough water to support the current population adequately. Decisions will have to be made on the best way to use water in a world where there is climate change. This free course looks at Water in the UK where water
Author(s): Creator not set

The science of nuclear energy
This free course, The science of nuclear energy, will delve into the science behind nuclear power and explain what happens inside a nuclear reactor and what it means for an element to be radioactive. It will explore some of the risks of producing nuclear power and examine the arguments for and against including it in future energy planning as well as looking at other potential future solutions. Author(s): Creator not set

Environment: understanding atmospheric and ocean flows
What affects the atmospheric and ocean flows? This free course, Environment: understanding atmospheric and ocean flows, explores the mechanisms that are important; the most rapid carrier is the wind. The basic principle of global atmospheric circulation is simple: warm air rises and cold air sinks. How does this principle affect the atmosphere and flow of water in practical terms? Starting with an iconic environmental icon, the polar bear, you will learn how global flows of water, heat and
Author(s): Creator not set

The Sun is the ultimate source of energy for the Earth's climate. A planet such as the Earth will have a stable temperature as long as there is a balance between the rate at which energy comes in from the Sun and the rate at which it is returned to space by the planet. If the two rates fail to match, the planet will either warm up or cool down until a balance is restored. Thus, it is appropriate to begin with a review of this global balancing act. The heart of the matter is that the energy fl
Author(s): The Open University

After studying this course, you should be able to:

• understand the physical basis of the natural greenhouse effect, including the meaning of the term radiative forcing

• know something of the way various human activities are increasing emmissions of the natural greenhouse gases, and are also contributing to sulphate aerosols in the troposphere

• demonstrate an awareness of the difficulties involved in the detection of any unusual global warming ‘signal
Author(s): The Open University

Before leaving office in 2008, Sir David King (the ex-Chief Scientific Advisor to the UK Government) introduced an ethical code for scientists. This drew particularly on his experience in working across the scientific–political divide on issues of climate change. The code comprises three attributes of scientific endeavour: rigour, representation and responsibility (Author(s): The Open University

For Iris Marion Young, the responsibility of those in North America and Europe towards distant others does indeed rest with their connections to injustices elsewhere, but it would be a mistake to stretch this line of reasoning too far. Although these connections, whether as a consumer, boardroom executive or shop manager, can establish a line of responsibility, as was claimed in Section 3.1, for Young this is only the starting point and not the end point of our involvement. We do not have to
Author(s): The Open University